Title: Some comments on unitary qubit lattice algorithms for classical problems

Journal Article · · Radiation Effects and Defects in Solids
 [1];  [1];  [1];  [2];  [3];  [4];  [5];  [6]
  1. College of William and Mary, Williamsburg, VA (United States)
  2. Old Dominion Univ., Norfolk, VA (United States)
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  4. Rogers State Univ., Claremore, OK (United States)
  5. National Technical University of Athens, Zographou (Greece)
  6. College of William and Mary, Williamsburg, VA (United States); National Technical University of Athens, Zographou (Greece)
+ Show Author Affiliations

A qubit lattice algorithm (QLA), which consists of a set of interleaved unitary collision-streaming operators, is developed for electromagnetic wave propagation in tensor dielectric media. External potential operators are required to handle gradients in the refractive indices, and these operators are typically non-unitary. A similar problem arises in the QLA for the Korteweg-de Vries equation, as the potential operator that models the KdV nonlinear term is also non-unitary. Further, several QLAs are presented here that avoid the need of this non-unitary potential operator by perturbing the collision operator. These QLAs are fully unitary.

Research Organization:
College of William and Mary, Williamsburg, VA (United States); Old Dominion Univ., Norfolk, VA (United States); Rogers State Univ., Claremore, OK (United States); Rogers State University, Claremore, OK (United States)
Sponsoring Organization:
Euratom Research and Training Program (WPEDU); USDO; USDOE
Grant/Contract Number:
FG02-91ER54109; SC0021647; SC0021651; SC0021653; SC0021857
OSTI ID:
1992524
Report Number(s):
DOE-RSU-SC0021653-10
Journal Information:
Radiation Effects and Defects in Solids, Journal Name: Radiation Effects and Defects in Solids Journal Issue: 1-2 Vol. 178; ISSN 1042-0150
Publisher:
Taylor and FrancisCopyright Statement
Country of Publication:
United States
Language:
English

References (33)

Relativistic Path Integral as a Lattice-based Quantum Algorithm journal February 2006
Lattice Boltzmann and quantum lattice gas representations of one-dimensional magnetohydrodynamic turbulence journal January 2003
Quantum lattice gas representation of some classical solitons journal April 2003
Benchmarking the Dirac-generated unitary lattice qubit collision-stream algorithm for 1D vector Manakov soliton collisions journal July 2016
Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media journal August 2019
Quantum lattice representations for vector solitons in external potentials journal March 2006
Unitary quantum lattice simulations for Maxwell equations in vacuum and in dielectric media journal October 2020
The Fermi–Pasta–Ulam problem: Fifty years of progress journal March 2005
Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms journal June 2021
On applications of quantum computing to plasma simulations journal September 2021
Reflection and transmission of electromagnetic pulses at a planar dielectric interface: Theory and quantum lattice simulations journal October 2021
Efficient quantum algorithm for dissipative nonlinear differential equations journal August 2021
Imaginary time integration method using a quantum lattice gas approach journal February 2016
Effect of Fourier transform on the streaming in quantum lattice gas algorithms journal February 2018
Unitary qubit lattice algorithms for spin-1 Bose Einstein condensates (BECs) journal February 2019
One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media I: theory journal February 2021
One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media. II: Simulations journal February 2021
Unitary qubit lattice simulations of complex vortex structures journal January 2012
Inelastic vector soliton collisions: a lattice–based quantum representation
  • Vahala, George; Vahala, Linda; Yepez, Jeffrey
  • Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 362, Issue 1821 https://doi.org/10.1098/rsta.2004.1415
journal June 2004
Solution of Maxwell's Equations in Terms of a Spinor Notation: the Direct and Inverse Problem journal March 1959
Application of Spinor Analysis to the Maxwell and Dirac Equations journal June 1931
Note on Light Quanta and the Electromagnetic Field journal August 1931
Quantum algorithm for the Vlasov equation journal December 2019
Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media journal April 2023
Poincaré recurrence and spectral cascades in three-dimensional quantum turbulence journal October 2011
Superfluid Turbulence from Quantum Kelvin Wave to Classical Kolmogorov Cascades journal August 2009
Quantum lattice gas algorithmic representation of gauge field theory conference October 2016
Vortex-antivortex pair in a Bose-Einstein condensate: Type-II quantum lattice gas as a nonlinear φ4 theory of a complex field journal April 2009
Unitary Qubit Lattice Gas Representation of 2D and 3D Quantum Turbulence book March 2012
Quantum Lattice Representation for the Curl Equations of Maxwell Equations dataset January 2024
Unitary Qubit Lattice Algorithm for Three-Dimensional Vortex Solitons in Hyperbolic Self-Defocusing Media dataset January 2019
Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media dataset January 2024
Reflection and transmission of electromagnetic pulses at a planar dielectric interface -- theory and quantum lattice simulations dataset January 2022

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Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Maxwell equations
anisotropic dielectric media
plasma
quantum th
quantumplasma
theory
unitary qubit algorithm